Book Image

Mathematics for Game Programming and Computer Graphics

By : Penny de Byl
5 (1)
Book Image

Mathematics for Game Programming and Computer Graphics

5 (1)
By: Penny de Byl

Overview of this book

Mathematics is an essential skill when it comes to graphics and game development, particularly if you want to understand the generation of real-time computer graphics and the manipulation of objects and environments in a detailed way. Python, together with Pygame and PyOpenGL, provides you with the opportunity to explore these features under the hood, revealing how computers generate and manipulate 3D environments. Mathematics for Game Programming and Computer Graphics is an exhaustive guide to getting “back to the basics” of mathematics, using a series of problem-based, practical exercises to explore ideas around drawing graphic lines and shapes, applying vectors and vertices, constructing and rendering meshes, and working with vertex shaders. By leveraging Python, Pygame, and PyOpenGL, you’ll be able to create your own mathematics-based engine and API that will be used throughout to build applications. By the end of this graphics focussed book, you’ll have gained a thorough understanding of how essential mathematics is for creating, rendering, and manipulating 3D virtual environments and know the secrets behind today’s top graphics and game engines.
Table of Contents (26 chapters)
1
Part 1 – Essential Tools
9
Part 2 – Essential Trigonometry
14
Part 3 – Essential Transformations
20
Part 4 – Essential Rendering Techniques

Viewing the Scene with Cameras

The camera is responsible for taking the coordinates of objects (specifically, all their vertices and other properties) and transforming them in the modelview of Figure 4.2. If you consider the vertices of the square mesh we looked at in the previous section, its coordinates are not going to retain those values as it will be moved around in the graphics/game world. The modelview takes the world location of the mesh and the location of the camera, as well as some additional properties, and determines the new coordinates of the mesh so that it can be rendered correctly. Note that I am being purposefully abstract in describing this process right now as there’s a lot of mathematics involved, and I don’t want to complicate the discussion at this point!

The camera is a virtual object through which the world is visualized. It is the eye of the viewer and can be moved around the environment to provide different points of view. As illustrated...